Alladi Ramakrishnan Hall

A hole-ographic spacetime

Borun D Chowdhury

Arizona State University, U. S. A

We embed spherical Rindler space – a geometry with a spherical
hole in its center – in asymptotically AdS spacetime and show that it
carries a gravitational entropy proportional to the area of the hole.
Spherical AdS-Rindler space is holographically dual to an ultraviolet
sector of the boundary field theory given by restriction to a strip of
finite duration in time. Because measurements have finite durations, local
observers in the field theory can only access information about bounded
spatial regions. We propose a notion of Residual Entropy that captures
uncertainty about the state of a system left by the collection of local,
finite-time observables. For two-dimensional conformal field theories we
use holography and the strong subadditivity of entanglement to propose a
formula for Residual Entropy and show that it precisely reproduces the
areas of circular holes in AdS3. Extending the notion to field theories on
strips with variable durations in time, we show more generally that
Residual Entropy computes the areas of all closed, inhomogenous curves on a
spatial slice of AdS3.